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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:20"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" target="_self">max+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" target="_self">max-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="mesfunc2.html#D2" target="_self">Def2</a>, <a class="ref" href="mesfunc2.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E3:20"/><b>then </b>
( <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" target="_self">max+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="extreal2.html#K1">max</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<a href="supinf_2.html#K1">0.</a>  &amp; <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" target="_self">max-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="extreal2.html#K1">max</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<a href="supinf_2.html#K1">0.</a>  )
 
<b>by </b><i><a class="ref" href="mesfunc2.html#D2" target="_self">Def2</a>, <a class="ref" href="mesfunc2.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:20"/>
( ( <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" target="_self">max+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> or <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" target="_self">max+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  ) &amp; ( <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" target="_self">max-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> or <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" target="_self">max-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  ) )
 <b>by </b><i><a class="ref" href="extreal2.html#T95">EXTREAL2:95</a></i>;<br/>


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